Diffraction of waves from obstacles are modelled by boundary value problems for the Helmholtz equation (as a prototype). In weak formulation we are led to certain classes of pseudodifferential operators in Sobolev spaces, which are invertible if the problems are well-posed. For so-called canonical configurations these operators can be analyzed in detail, sometimes explicitly inverted. This survey lecture presents precise relations between the operators in game and gives an idea of their nature and possible treatment.